A333410 a(n) is the smallest positive integer not yet appearing in the sequence such that n*a(n) contains n as a substring.

1, 6, 10, 11, 3, 16, 21, 23, 22, 31, 100, 26, 87, 51, 41, 73, 69, 66, 63, 36, 58, 101, 97, 52, 5, 102, 103, 46, 79, 61, 107, 76, 192, 151, 81, 38, 201, 89, 164, 35, 59, 34, 173, 126, 99, 184, 74, 135, 153, 7, 167, 176, 29, 251, 121, 28, 168, 148, 27, 56, 92, 123, 137, 57, 141, 207, 25, 113

Offset: 1

Author

Scott R. Shannon, Apr 11 2020

Keywords

• nonn
• base

Examples

			a(2) = 6 as 6 has not appeared previously and 2 * 6 = 12 which contains '2' as a substring.
a(6) = 16 as 16 has not appeared previously and 6 * 16 = 96 which contains '6' as a substring.
a(7) = 21 as 21 has not appeared previously and 7 * 21 = 147 which contains '7' as a substring.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A333410

Crossrefs

Cf. A086064, A333774, A333775, A333811, A332795, A332703.

Programs

PARI

See Links section.

Python

from itertools import count, islice
def agen(): # generator of terms
    s, mink, aset, concat = 1, 2, {1}, "1"
    yield from [1]
    for n in count(2):
        an, sn = mink, str(n)
        while an in aset or not sn in str(n*an): an += 1
        aset.add(an); s += an; concat += str(an); yield an
        while mink in aset: mink += 1
print(list(islice(agen(), 68))) # Michael S. Branicky, Feb 08 2024